Intracellular transport in eukarya is attributed to motor proteins that transduce chemical energy into directed mechanical energy. This suggests that, in nonequilibrium systems, fluctuations may be oriented or organized to do work. Here we seek to understand how this is manifested by quantitative mathematical portrayals of these systems.
Mots clés : Fokker-Planck, weakly coupled system, molecular motor, brownian rachet, transport
@article{M2AN_2004__38_6_1011_0, author = {Chipot, Michel and Hastings, Stuart and Kinderlehrer, David}, title = {Transport in a molecular motor system}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {1011--1034}, publisher = {EDP-Sciences}, volume = {38}, number = {6}, year = {2004}, doi = {10.1051/m2an:2004048}, mrnumber = {2108942}, zbl = {1077.35060}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2004048/} }
TY - JOUR AU - Chipot, Michel AU - Hastings, Stuart AU - Kinderlehrer, David TI - Transport in a molecular motor system JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 1011 EP - 1034 VL - 38 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004048/ DO - 10.1051/m2an:2004048 LA - en ID - M2AN_2004__38_6_1011_0 ER -
%0 Journal Article %A Chipot, Michel %A Hastings, Stuart %A Kinderlehrer, David %T Transport in a molecular motor system %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 1011-1034 %V 38 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2004048/ %R 10.1051/m2an:2004048 %G en %F M2AN_2004__38_6_1011_0
Chipot, Michel; Hastings, Stuart; Kinderlehrer, David. Transport in a molecular motor system. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 6, pp. 1011-1034. doi : 10.1051/m2an:2004048. http://www.numdam.org/articles/10.1051/m2an:2004048/
[1] Mouvement induit par un potentiel périodique de basse symétrie : diélectrophorèse pulse. C. R. Acad. Sci. Paris II 315 (1992) 1653.
and ,[2] Thermodynamics and kinetics of a Brownian motor. Science 276 (1997) 917-922.
,[3] A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84 (2000) 375-393. | Zbl
and ,[4] A variational principle for molecular motors. Meccanica 38 (2003) 505-518. | Zbl
, and ,[5] Rotary DNA motors. Biophys. J. 69 (1995) 2256-2267.
, and ,[6] Remarks about the flashing rachet, in Proc. PASI 2003 (to appear). | MR | Zbl
, and ,[7] The kinetic cycles of myosin, kinesin, and dynein. Ann. Rev. Physiol. 58 (1996) 731-750.
,[8] Remarks about diffusion mediated transport: thinking about motion in small systems. (to appear). | MR | Zbl
and ,[9] Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates, Inc. (2001).
,[10] Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7 (1957) 255-318.
,[11] The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998) 1-17. | Zbl
, and ,[12] Diffusion-mediated transport and the flashing ratchet. Arch. Rat. Mech. Anal. 161 (2002) 149-179. | Zbl
and ,[13] Approximation of parabolic equations based upon Wasserstein's variational principle. ESAIM: M2AN 33 (1999) 837-852. | Numdam | Zbl
and ,[14] Compound matrices and ordinary differential equations. Rocky Mountain J. Math. 20 (1990) 857-872. | Zbl
,[15] A processive single-headed motor: kinesin superfamily protein KIF1A. Science 283 (1999) 19.
and ,[16] Mechanism of the single headed processivity: diffusional anchoring between the K-loop of kinesin and the C terminus of tubulin, in Proc. Nat. Acad. Sciences 7 (2000) 640-645.
and ,[17] Dynamics of labyrinthine pattern formation: a mean field theory. Arch. Rat. Mech. Anal. 141 (1998) 63-103. | Zbl
,[18] The geometry of dissipative evolution equations: the porous medium equation. Comm. PDE 26 (2001) 101-174. | Zbl
,[19] Dynamics of a light driven molecular motor. Mol. Cryst. Liq. Cryst. 375 (2002) 577-591.
, and ,[20] Energy transduction of isothermal ratchets: generic aspects and specific examples close and far from equilibrium. Phys. Rev. E 60 (1999) 2127-2140.
, , and ,[21] The correlation ratchet: a novel mechanism for generating directed motion by ATP hydrolysis, in Cell Mechanics and Cellular Engineering, V.C Mow et al. Eds., Springer, New York (1995).
, and ,[22] Maximum principles in differential equations, Prentice Hall, Englewood Cliffs, N.J. (1967). | MR | Zbl
and ,[23] Brownian motors: noisy transport far from equilibrium. Phys. Rep. 361 (2002) 57-265. | Zbl
,[24] Molecular Motors. Wiley-VCH Verlag, Wennheim (2003).
,[25] Totally positive differential systems. Pacific J. Math. 32 (1970) 203-230. | Zbl
,[26] A one phase Stefan problem via Monge-Kantorovich theory. CNA Report 03-CNA-007.
,[27] The way things move: looking under the hood of motor proteins. Science 288 (2000) 88-95.
and ,[28] Topics in optimal transportation, Providence. AMS Graduate Studies in Mathematics 58 (2003). | MR | Zbl
,[29] Nonlinear functional analysis and its applications. I Springer, New York (1986). | MR | Zbl
,Cité par Sources :